Answer:
[tex]x(x+2)(x-15)[/tex]
Step-by-step explanation:
we have
[tex]x^{3}-13x^{2}-30x[/tex]
step 1
Factor x
[tex]x^{3}-13x^{2}-30x=x(x^{2}-13x-30)[/tex]
step 2
Find the solutions of [tex](x^{2}-13x-30)[/tex]
Complete the square
[tex](x^{2}-13x)=30[/tex]
[tex](x^{2}-13x+6.5^{2})=30+6.5^{2}[/tex]
[tex](x^{2}-13x+42.25)=72.25[/tex]
[tex](x-6.5)^{2}=72.25[/tex]
square root both sides
[tex](x-6.5)=(+/-)8.5[/tex]
[tex]x=6.5(+/-)8.5[/tex]
[tex]x1=6.5(+)8.5=15[/tex]
[tex]x2=6.5(-)8.5=-2[/tex]
so
[tex](x^{2}-13x-30)=(x+2)(x-15)[/tex]
substitute
[tex]x^{3}-13x^{2}-30x=x(x+2)(x-15)[/tex]
